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Mirrors > Home > ILE Home > Th. List > ax11  Structured version Unicode version 
Description: Axiom of Variable
Substitution. One of the 5 equality axioms of predicate
calculus. The final consequent is a way of
expressing "
substituted for in
wff " (cf.
sb6 1686). It
is based on Lemma 16 of [Tarski] p. 70 and
Axiom C8 of [Monk2] p. 105,
from which it can be proved by cases.
Variants of this axiom which are equivalent in classical logic but which have not been shown to be equivalent for intuitionistic logic are ax11v 1629, ax11v2 1622 and ax11o 1625. (Contributed by NM, 5Aug1993.) 
Ref  Expression 

ax11 
Step  Hyp  Ref  Expression 

1  vx  . . 3  
2  vy  . . 3  
3  1, 2  weq 1331  . 2 
4  wph  . . . 4  
5  4, 2  wal 1272  . . 3 
6  3, 4  wi 4  . . . 4 
7  6, 1  wal 1272  . . 3 
8  5, 7  wi 4  . 2 
9  3, 8  wi 4  1 
Colors of variables: wff set class 
This axiom is referenced by: ax10o 1525 equs5a 1596 sbcof2 1612 ax11o 1624 ax11v 1629 
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